Answer : The mass of benzyl salicylate needed to manufacture 290 tubes of sunscreen are, 1.18 kg
Explanation :
As we are given that a sunscreen preparation contains 2.40 % by mass benzyl salicylate. That means, 2.40 grams of benzyl salicylate present in 100 g of solution.
First we have to convert the given mass from oz into kg.
Conversion used:
1 kg = 35.274 oz
or,
[tex]1oz=\frac{1}{35.274}kg[/tex]
So,
[tex]6oz=\frac{6oz}{1oz}\times \frac{1}{35.274}kg=0.1701kg[/tex]
Now we have to determine the mass of benzyl salicylate.
As, 100 g of solution contains mass of benzyl salicylate = 2.40 g
So, 0.1701 kg of solution contains mass of benzyl salicylate = [tex]\frac{2.40g}{100g}\times 0.1701kg=0.00408kg[/tex]
Now we have to determine the mass of benzyl salicylate are needed to manufacture 290 tubes of sunscreen.
Mass of benzyl salicylate in 290 tubes of sunscreen = 0.00408 kg × 290
Mass of benzyl salicylate in 290 tubes of sunscreen = 1.18 kg
Thus, the mass of benzyl salicylate needed to manufacture 290 tubes of sunscreen are, 1.18 kg
To prepare 290 tubes that contain 6.0 oz of sunscreen that is 2.40% by mass benzyl salicylate, we need 1.2 kg of benzyl salicylate.
First, we will calculate the mass in kilograms of 290 tubes of sunscreen considering the following relationships.
[tex]290Tube \times \frac{6.0oz}{1Tube} \times \frac{1kg}{35.27oz} = 49kg[/tex]
The sunscreen preparation contains 2.40 % by mass benzyl salicylate, that is, there are 2.40 kg of benzyl salicylate every 100 kg of sunscreen.
The mass of benzyl salicylate in 49 kg of sunscreen is:
[tex]49kgSunscreen \times \frac{2.40kgBS}{100kgSunscreen} = 1.2kgBS[/tex]
To prepare 290 tubes that contain 6.0 oz of sunscreen that is 2.40% by mass benzyl salicylate, we need 1.2 kg of benzyl salicylate.
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